find the exact value of $\tan^{-1}left(-\frac{sqrt{3}}{3}\right)$. write your answer in radians in terms of…

find the exact value of $\tan^{-1}left(-\frac{sqrt{3}}{3}\right)$. write your answer in radians in terms of $pi$. $\tan^{-1}left(-\frac{sqrt{3}}{3}\right)=$

find the exact value of $\tan^{-1}left(-\frac{sqrt{3}}{3}\right)$. write your answer in radians in terms of $pi$. $\tan^{-1}left(-\frac{sqrt{3}}{3}\right)=$

Answer

Explanation:

Step1: Recall the range of inverse - tangent function

The range of $y = \tan^{-1}(x)$ is $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.

Step2: Find the angle whose tangent is $-\frac{\sqrt{3}}{3}$

We know that $\tan\left(-\frac{\pi}{6}\right)=-\frac{\sqrt{3}}{3}$ and $-\frac{\pi}{6}\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.

Answer:

$-\frac{\pi}{6}$